Cosine fun

Geometry Level 3

If \(128\cos^{8}10^{\circ } - 256\cos^{6} 10^{ \circ} + 160 \cos^{4} 10^{\circ } - 32\cos^{2} 10^{\circ } + 1\) can be expressed in the form \(\cos x^{ \circ}\) for a positive angle \(x^\circ\), then what is the value of \( x \)?

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